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<TITLE>Re: [RASMB] hydrodynamic non-ideality</TITLE>
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<BLOCKQUOTE>Hi Mitra (and all)<BR>
<BR>
Provided that one is working in pH conditions not too far from neutrality, and that the neutral salt concentration is of the order of 100 mM, then one gets an excellent estimate for ks from the relationship<BR>
<BR>
ks = 2*vbar*((Vs/vbar) + F^3) <BR>
<BR>
where Vs/vbar is the swelling ratio - around 1.4 is a good guess for most proteins) and F is the frictional ratio f/f0. ks is found from the <I>limiting</I> slope of the s vs c curve, in practice better estimated from the 1/s vs c curve. Optimally one uses the extended form of the s vs c equation (see my chapter in the 1992 AUC book - in which there is, sad to say, a typo in the equation), but up to around 10 mg/mL or so it makes very little difference. The method of fitting an "isotherm" over the range of c works well even with weak interactions (see e.g. Patel, Trushar R, Harding, Stephen E, Ebringerova, Anna, Deszczynski, Marcin, Hromadkova, Zdenka, Togola, Adiaratoou, Paulsen, Bert Smestad, Morris, Gordon, A and Rowe, Arthur J ( 2007) Weak Self-Association in a Carbohydrate System Biophysical Journal 93 741-749), but clearly the interaction you have got is not all that weak.<BR>
<BR>
I am working on a more extended form of my own fitting function - in particular I have realised that at the moment it contains one too many parameters in the general c-dependence equation! As and when I get it completed, I will have a go and see what it does with your data.<BR>
<BR>
Anyhow - the answers to your queries are (2) AGREED and (3) YES.<BR>
<BR>
Kind regards<BR>
<BR>
Arthur<BR>
<BR>
<BR>
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*******************************************************<BR>
Arthur J Rowe<BR>
Professor of Biomolecular Technology<BR>
NCMH Business Centre<BR>
University of Nottingham<BR>
School of Biosciences<BR>
Sutton Bonington<BR>
Leicestershire LE12 5RD UK<BR>
<BR>
Tel: +44 (0)115 951 6156<BR>
+44 (0)116 271 4502<BR>
Fax: +44 (0)115 951 6157<BR>
email: arthur.rowe@nottingham.ac.uk<BR>
Web: www.nottingham.ac.uk/ncmh/business<BR>
*******************************************************<BR>
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<BLOCKQUOTE><TT>Hi All<BR>
<BR>
Is there anyway I can ignore the hydrodynamic non-ideality? After all <BR>
my protein concentrations only go up to ~ 12 mg/ml! :)<BR>
<BR>
Ok that was said in jest or may be half jest since ignoring the ks of <BR>
0.009 ml/mg seems to allow me to explain my velocity data by a simple <BR>
monomer-trimer equilibrium.<BR>
<BR>
More seriously though -<BR>
1. For an isodesmic association model (either the good old N^2(/3) <BR>
approach used by Timasheff or the more recent bead modeling used by <BR>
Sontag et al. 2004 Biophys. Chem. both used for tubulin <BR>
self-association) the s20,w for the oligomers are fixed a priori to <BR>
any curve fitting (whether Delta C in SEDANAL or the isotherm)<BR>
<BR>
2. Using the Rowe derivation for ks - one should be theoretically able <BR>
to calculate the ks for a given f/f0. Since according to point 1 the <BR>
s20,w water for the oligomers is already assumed to be known, one can <BR>
calculate the f/f0 for each of the oligomers (I guess this only <BR>
applies to bead modeled oligomers since the basis for N^(2/3) is a <BR>
constant f/f0).<BR>
<BR>
3. Bottomline - can one use the Rowe equation to calculate the ks for <BR>
each of the oligomers and then use this value for fitting the weight <BR>
average isotherm? Or am I missing something crucial and there is a <BR>
fundamental problem with this approach? Or for the sake of simplicity <BR>
can I just presume a ks of 0.009 ml/mg for all oligomers and fit the <BR>
data.<BR>
<BR>
If anyone wishes or has the time for it - here are the numbers -<BR>
0.03(4.57), 0.37(4.77), 0.745 (5.00), 1.4 (5.3), 3.39 (5.86), 6.65 <BR>
(6.51), 12.2 (6.99).<BR>
The first number is [P] in mg/ml and in brackets the weight-average <BR>
s20,w. The best fit I have so far is for a modeled isodesmic <BR>
assocation with the relation ln(sn/s1) = 0.5781 ln n - 0.0493 (ln n)^2 <BR>
. s1 (20,w) ~ 4.53S ks=0.009 mg/ml. Fitted by sedanal Kiso=1.37x10^4. <BR>
Isotherm = 1.29x10^4.<BR>
<BR>
Any and all thoughts are welcome. Have a good weekend.<BR>
Mitra<BR>
<BR>
<BR>
<BR>
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